Correlation functions for the detection of Wigner molecules in a one-channel Luttinger liquid quantum dot

Abstract

In one-channel, finite-size Luttinger one-dimensional quantum dots, both Friedel oscillations and Wigner correlations induce oscillations in the electron density with the same wavelength, pinned at the same position. Therefore, observing such a property does not provide any hint about the formation of a Wigner molecule when electrons interact strongly and other tools must be employed to assess the formation of such correlated states. We compare here the behavior of three different correlation functions and demonstrate that the integrated two point correlation function, which represents the probability density of finding two particles at a given distance, is the only faithful estimator for the formation of a correlated Wigner molecule.

arXiv comment6 pages, 5 figures

References in corpus (47)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Spins in few-electron quantum dots
• One-Dimensional Fermi liquids
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Exploring phase coherence in a 2D lattice of Bose-Einstein condensates
• Effective low-energy theory for correlated carbon nanotubes
• Wigner Crystal in One Dimension
• Interacting one dimensional electron gas with open boundaries
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Observation of a One-Dimensional Spin-Orbit Gap in a Quantum Wire
• Experimental Evidence for Resonant-Tunneling in a Luttinger-Liquid
• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• Conductance of a quantum wire in the Wigner crystal regime
• The spin-incoherent Luttinger liquid
• Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube
• Ground state properties of the one dimensional Coulomb gas
• Tomonaga-Luttinger physics in electronic quantum circuits
• Interacting electrons with spin in a one-dimensional wire connected to leads
• Density functional theory in one-dimension for contact-interacting fermions
• Coulomb drag between two spin incoherent Luttinger liquids
• Wigner crystal vs. Friedel oscillations in the 1D Hubbard model
• Tunneling between helical edge states through extended contacts
• Coulomb versus spin-orbit interaction in few-electron carbon-nanotube quantum dots
• AFM probe for the signatures of Wigner correlations in the conductance of a one-dimensional quantum dot
• Correlated electrons in optically-tunable quantum dots: Building an electron dimer molecule
• Transport properties of quantum dots in the Wigner molecule regime
• Universality of electron correlations in conducting carbon nanotubes
• Transport through a quantum spin Hall quantum dot
• Coulomb blockade microscopy of spin density oscillations and fractional charge in quantum spin Hall dots
• Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization
• Asymmetric Zero-Bias Anomaly for Strongly Interacting Electrons in One Dimension
• Charge and spin addition energies of one dimensional quantumn dot
• Bosonization of strongly interacting electrons
• Imaging and manipulating electrons in a 1D quantum dot with Coulomb blockade microscopy
• Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions
• Signatures of Wigner Localization in Epitaxially Grown Nanowires
• Deformed Wigner crystal in a one-dimensional quantum dot
• Helical nuclear spin order in two-subband quantum wires
• Temperature-induced emergence of Wigner correlations in a STM-probed one-dimensional quantum dot
• Topological Insulator Magnetic Tunnel Junctions: Quantum Hall Effect and Fractional Charge via Folding
• 2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement
• Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot
• Magnetic AC control of the spin textures in a helical Luttinger liquid
• Dynamic correlations of the Coulomb Luttinger liquid

Cited by in corpus (17)

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• Crystallization of Levitons in the fractional quantum Hall regime
• Hong-Ou-Mandel characterization of multiply charged Levitons
• Out of equilibrium density dynamics of a quenched fermionic system
• Non-monotonic response and light-cone freezing in gapless-to-(partially) gapped quantum quenches of fermionic systems
• One-dimensional few-electron effective Wigner crystal in quantum and classical regimes
• Fractional charge oscillations in quantum spin Hall quantum dots
• Fermionic versus bosonic behavior of confined Wigner molecules
• Spectral properties of interacting helical channels driven by Lorentzian pulses
• Towards a phase diagram of the topologically frustrated XY chain
• Crystallization of fractional charges in a strongly interacting quasi-helical quantum dot
• The invisible Majorana bound state at the helical edge
• Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains
• Collective ground states in small lattices of coupled quantum dots
• Coherent charge and spin oscillations induced by local quenches in nanowires with spin-orbit coupling
• Density-density Correlation Function of Strongly Inhomogeneous Luttinger Liquids
• Few-body precursors of topological frustration